Plot the functions (G(a) and Y(a)) in diagram using Python without using 'contour' function, just use 'plot' function or others instead.

You could plot points and connect the point to make the contour lines. G(a)=(a_1)*(a_2)^2 and Y(a):= Y_1 (a) = (a_1)^2 +(a_2)^2 - 1 for a = (a_1, a_2)^T \in R^2. G(a) converges to min if subject to the constraint Y(a)=0. By solving the function, we can get G(a) attains its global minimum at (-sqrt(),+/- (2/sqrt(3))^T, and the point (sqrt(2),0)^T yields a local minimum.